1. Field of the Invention
The present invention relates to an optical scanning lens and an optical scanning and imaging system for use in an optical scanning apparatus for scanning a surface of an optical recording medium, such as a photosensitive material, for writing data thereupon, and, in particular, to an optical scanning lens and an optical scanning and imaging system which is constructed to produce a minimum beam spot diameter, in a sub-scanning direction, within a desired range; to reduce variation in a scanning line pitch; and to reduce variation in beam spot diameter according to an image height for every point along a scanning surface, which variations are caused by non-uniformity of the refractive index in a lens used in the optical scanning imaging system.
2. Description of the Related Art
An optical scanning apparatus for scanning a surface of an optical recording medium, such as a photosensitive material, for writing data thereupon, is well known in relation to digital copying machines, laser printers, or the like.
In such an optical scanning apparatus, a usual optical arrangement is such that a laser beam from a light source is deflected by a rotating light deflector, such as a polygon mirror, and the deflected light then is transmitted to a scanning and image forming lens system such that the light is converged to form a light spot or beam spot to be applied on a surface to be scanned for scanning the surface for writing data thereupon. The scanning lens is therefore required to meet constant velocity characteristics such as f.theta. characteristics and various optical characteristics including correction of curvature of field. Also, in such an optical scanning apparatus, the system of lenses for scanning and image formation which converges a light beam deflected by a light deflector as a light spot or beam spot on a scanned surface has been designed based on the assumption that the refractive index inside a lens is constant.
However, as described below, the plastics molding lens forming process used to form such a lens often leads to a variable refractive index inside the lens which causes many problems described in more detail below.
It has been difficult to achieve the required and desired lens characteristics solely by forming the surface of the lens system to have a spherical surface. Thus, it has been recently attempted to provide a lens having a special surface such as a non-spherical surface to achieve the necessary optical characteristics.
Such a lens having a non-spherical surface is generally manufactured using a plastics molding process. When a lens is made using the plastics molding process, molten plastics material is poured into a mold having a desired pattern for a lens surface. When the molten plastics in the mold is cooled, the temperature of the plastics gradually decreases starting from the part of the plastics material which is in contact with a surface of the mold and extending toward the inner-most part of the plastics material in the mold which is located farthest away from the mold surface. Therefore, differences in the temperature of the plastics material arise, especially between a center potion of the lens and a peripheral portion of the lens. Due to this difference in the temperature, some of the molten plastics material moves toward the part of the mold where the temperature has decreased or is the lowest. As a result, when the molded plastics material is completely cooled, the density of the plastics material is higher at the peripheral portions of the lens where the temperature had started to decrease earlier than the center portion of the lens where the temperature started to decrease later than the peripheral portions.
Thus, when a lens is produced with a plastics molding process, the density of the inner portion of the lens is lower than the density of the outer-circumferential portion thereof due to the influence of a temperature difference between the inner part and the outer circumferential part thereof, which occurs when the lens is cooled in a mold. This phenomenon produces a non-uniform density of plastics material in the inner part of the aspherical lens.
Such non-uniformity of density of plastics causes non-uniformity of the refractive index in the lens. The refractive index is high where the density of plastics is high. Therefore, the refractive index of the peripheral portions of the lens is higher than the refractive index of the center portion.
The non-uniformity of the refractive index affects the optical characteristics of the lens and causes the optical performance of a system of lenses for scanning and image formation to be different from a desired level. In addition, the non-uniformity causes variation in scanning line pitch and diameter of a light spot or beam spot according to an image height. Furthermore, the non-uniformity of the refractive index is increased if cooling time is shortened. This makes it difficult to reduce the time and cost required to make the lens using the plastics molding process which is necessary to make a non-spherical lens.
The optical scanning and image forming lens is shaped so as to function as an image forming lens for a deflected light flux. Therefore, the lens is generally formed to have a shape which has a shorter width in a direction corresponding to the sub-scanning direction on the optical path from the light source to the scanned surface. Consequently, a decrease in temperature occurs rapidly at both end parts of the lens in the sub-scanning direction. As a result, the variation of the refractive index in the lens is increased in the sub-scanning direction. Thus, the optical performance in the sub-scanning direction is especially affected.
FIGS. 25(a)-25(e) are schematic drawings and charts illustrating an example of a distribution of refractive indices in a scanning lens.
FIG. 25(a) is a schematic drawing illustrating an example of a distribution of refractive indices in an optical lens 1 in the main scanning direction at a virtual cross section of the optical lens 1 in a plane which includes the optical axis and is perpendicular to the scanned surface, illustrated via contour lines. Each contour line in the FIGS. 25(a)-25(e) indicates a line where the refractive index changes. FIG. 25(b) is a drawing illustrating a distribution of refractive indices in the main scanning direction at the virtual cross section illustrated in FIG. 25(a) at the center portion of the thickness-wise direction of the lens, which is indicated by a line-and-dot line in FIG. 25(a). FIG. 25(c) is a drawing illustrating distribution of refractive indices of the lens 1 in the sub-scanning direction at a virtual cross section of the lens 1 in a plane which includes the optical axis and is parallel to the sub-scanning direction, illustrated via contour lines. FIG. 25(d) is a drawing illustrating distribution of refractive indices at the virtual cross section in a plane parallel to the sub-scanning direction including the optical axis. FIG. 25(e) is a drawing illustrating distribution of refractive indices at a cross section at the center of the thickness-wise direction of the lens in FIG. 25(c).
As illustrated in FIGS. 25(a)-25(e), the refractive index in the lens becomes greater at increasing distances from a center towards the peripheral parts of the lens. This is due to the peripheral parts of the lens being cooled more rapidly than the central part of the lens. As a result, the density of the plastics in the peripheral parts of the lens becomes high compared to the central part of the lens.
An optical scanning and image forming lens system is generally designed, regardless of whether the lens system is made of plastics or includes a plastic lens, based upon the assumption that the refractive index in the lens is uniform. Therefore, if the distribution of the refractive index is not uniform, then the lens system will not perform according to desired optical characteristics. Accordingly, when designing a lens system including a plastic lens, for accomplishing a desired optical performance with the lens system, careful consideration needs to be given to distribution of refractive indices in the lens.
Japanese laid-open patent application No. 9-49976 discloses an example of an optical scanning and image forming lens system in which consideration is given to distribution of refractive indices in the lens. In this example, the diameter of a light spot or beam spot in the sub-scanning direction is minimized by forming an image plane having a least wave-front aberration in the sub-scanning direction at the surface to be scanned by considering the distribution of refractive indices in the lens.
Although the scanning lens described in Japanese laid-open patent application No. 9-49976 has a positive power, the refractive index is greater at locations closer to the peripheral portions as compared to locations closer to the center portion of the lens as described above. Therefore, a converging position of a light spot or beam spot, which needs to be located precisely at the surface to be scanned, generally shifts to a position which is spaced away from a desired position relative to a light deflector. To correct for this phenomenon, the position of the lens in Japanese laid-open patent application No. 9-49976 is shifted in one direction by an amount which is not specified.
In such lenses, the diameter of a light spot or beam spot which scans the surface to be scanned changes as the image height changes in accordance with curvature of field of the optical scanning lens. Further, if the refractive index is not uniform in the lens, the diameter of the light spot is also varied due to the non-uniform distribution of the refractive indices in the lens.
FIG. 27 is a drawing explaining that the diameter of a light spot used to scan the surface to be scanned increases when the distribution of refractive indices of the optical scanning lens is not uniform. In FIG. 27, the vertical axis indicates a size of the diameter of a light spot on the surface to be scanned and the horizontal axis indicates an amount of defocusing (a distance between an image forming position, i.e., a converging position, of a light spot and the position of the surface to be scanned).
When the distribution of the refractive index is uniform in the optical scanning lens, the relation between the defocusing amount and the diameter of a light spot is as indicated by the dotted line in the FIG. 27 and the diameter of the light spot is minimum at the surface to be scanned. When the distribution of the refractive index is not uniform in the lens, the relation between the defocusing amount and the diameter of the light spot is as indicated by the solid line in FIG. 27. As illustrated in the FIG. 27, the diameter of the light spot at the surface to be scanned is larger than the diameter as designed by a length indicated by L when the distribution of the refractive index of the lens is not uniform.
Therefore, when designing a scanning lens, if the distribution of refractive indices in the lens is not considered, variation in the diameter of a light spot according to the image height increases, which consequently deteriorates the quality of an image to be formed by optical scanning through the scanning lens.
As described above, an optical scanning and image forming lens system is generally designed, regardless of whether the lens system is made of plastics or includes a plastic lens, based upon the assumption that the distribution of the refractive index in the lens is uniform. Therefore, if the distribution of the refractive index is not uniform, then the lens system will not perform according to the designed optical characteristics. Accordingly, when designing a lens system including a plastic lens, for accomplishing a desired optical performance with the lens system, careful consideration needs to be given to the distribution of refractive indices in the lens.
As one of the important characteristic of an optical scanning device, a scanning line pitch, that is, a distance between neighboring scanning lines, is required to be constant. When the scanning line pitch is not uniform, an image written as a result of the scanning will be distorted due to scanning line pitch variation. Therefore, for writing a high quality image, the scanning pitch variation needs to be minimized.
The scanning line pitch variation is mainly caused by a surface inclination of a polygon mirror used as a deflector. When a deflecting reflective surface of the polygon mirror is not substantially parallel to the rotating axis of the polygon mirror, then a deflected beam is shifted to the sub-scanning direction according to the inclination of each deflecting reflective surface. As a result, the image forming position of the light beam is dislocated in the sub-scanning direction on the surface to be scanned, thus causing variation in the scanning line pitch.
A prior art method of correcting scanning line pitch variation is a so-called surface inclination correction method. In the surface inclination correction method, a beam from the light source is formed as a linear image elongated in the main scanning direction located near a deflecting reflective surface of a polygon mirror and a conjugate relationship is established via an optical scanning and imaging system located between the position near the deflecting reflective surface of the polygon mirror and the position of the scanning surface.
However, when the refractive index of a lens used in the scanning and imaging system is not uniform, even when the above surface inclination correction method is performed, if the refractive index distribution in the lens is not considered and compensated for in the correction process, scanning line pitch variation is caused by the non-uniformity of the refractive index in the lens.
Further, because the rotational axis of the deflecting reflective surface of the polygon mirror deviates from the surface of the polygon mirror, the imaging position of the linear image is deviated from the deflecting reflective surface as the surface is rotated, causing a so-called sag problem. Therefore, for minimizing the variation in scanning line pitch, the effect of sag on the line pitch needs to be considered.
Moreover, there is an increasing demand for a smaller diameter of a light spot along with a request for high-density image recording to be achieved by an optical scanning apparatus. It is therefore required to properly correct curvature of field and spherical aberration of the lens. For correcting spherical aberration properly, an effective way is to reproduce "given designed distribution of refractive indices" inside a lens. However, it is difficult to realize the distribution of refractive indices as designed.
Distribution of refractive indices inside a lens occurring during the plastics molding process described above and distribution of refractive indices inside a lens which is defined as a design condition do not correspond precisely but are uncertain or variable to some extent. As a result, it is difficult to improve the yield of a scanning and image forming lens so as to have a high enough finished product quality to be put to practical use. Consequently, it is difficult to reduce the costs of a system of lenses for scanning and image formation and an overall cost of an optical scanning apparatus.